مقیاس بزرگی محلی (ML) برای البرز مرکزی

The availability of a large amount of the data recorded by the Iranian Seismic Telemetry Network (ISTN) has motivated this study to develop relations for the routine determination of M_L scale for Central Alborz region of northern Iran. The M_L is commonly used in engineering because it is determined within the frequency range (0.5-3 sec) of interest in most of such applications. For any comprehensive seismic hazard analysis, one needs a calibrated magnitude relationship as well as an earthquake catalog for the study region. It is a well-known fact that the regional geology has a great influence on magnitude relations. Therefore, for each seismic region a specific magnitude relation has to be developed. The M_L scale is based on the arithmetic mean of horizontal components of the synthesized Wood–Anderson seismograms. We used both nonparametric and parametric methods for inversion. We used a large dataset of 3886 events including 62031 waveforms which recorded by Tehran, Semnan and Sari seismic networks during 02/03/1997 to 13/03/2011. These seismic networks comprise of 19 three-component stations. We calculated the associated synthesized Wood-Anderson seismogram for each SS-1 waveform which records the velocity. Based on Richter’s method, we used amplitudes which are arithmetic means of those of horizontal components.
Richter’s M_L formula first developed for southern California and Savage and Anderson introduced a nonparametric least-squares inversion method which has been used by others. In this method, the amplitudes recorded at arbitrary distances are linearly interpolated to yield values for the attenuation curve at some fixed distances. In this study, we used both methods.
The resulting equations are -logA₀ = 0.9819log(r / 100) + 0.0028(r - 100) + 3.0 and-logA₀ = 1.076log(r) + 0.0029(r) + 0.5580 from parametric and non-parametric methods, respectively. Where r is hypocentral in kilometer and A₀ is amplitude in millimeter. The two methods yielded very similar results. Unlike the parametric method, the nonparametric one does not impose any a priori assumption of the shape of the attenuation curve on the data and has the potential to detect hinges in the attenuation curve that are caused by structural boundaries such as Moho or geological variations affects on the attenuation curve. Thus the result obtained by nonparametric method was chosen as the final result.
Bakun and Joyner (1984) give the following formula for the Q / f  ratio: taking an average S-wave crustal velocity of V_S = 3.3 km/sec, the k value obtained by the non-parametric method, 0.0029, would imply a Q / f  ratio of 150 in Central Alborz, Iran.